Other than a pilot or flight attendant, what are some other job options in the airline industry?

I am in Airlines sales working with corporate accounts as well as calling on large travel agencies. Like any corporation we have many levels of jobs in computer science and Math related jobs. We have a marketing department. We also have a reservations center in Vancouver Canada.

Airlines employ people at all levels of education as well as many different vocations. The airline industry in general also impacts other businesses and varying types of industry that support it.
Some other areas within an airline might be HR, operations management, scheduling, FAA certified dispatcher, purchasing, business forecasting, aircraft mechanics, and project management.
Areas that support the airlines can include engine and equipment manufacturers, airport operations, ramp personnel, fuelers, catering, maintenance staff, county employee's that work with the airports, US Customs, TSA, FAA, etc.
One really good way to break into being around aircraft is to spend time at a local airport and see about fueling airplanes. Doesn't pay much, but really introduces you to airplane operations on a small scale. You can also apply to airlines as a ramp agent. Aviation really does have many interesting jobs and side industries that support it. Just start looking, you will find something.

Gate agent, ground crew, catering for the planes, restaurant server in airport restaurants, airport authority office

There are many other positions at airlines. Airline management is one option. Another option would be to become a mechanic for an airline, however many times those jobs are outsourced to a contractor to provide the maintenance services. Finally, you could become an licensed dispatcher for an airline. These people plan flights and work with crews to get weather information and comply with federal aviation regulations.